document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80375>Question 80375</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495105104/algebrahomeworkh>Algebra for college students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the Inverse of the function f(x)= 2/3x -3/5.<BR>\n" );
document.write( "I know the answer is f-1(x)= -6-x<BR>\n" );
document.write( "                             -----           <BR>\n" );
document.write( "                               3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I only need to know the solution on how it was figured out.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57678 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282%2F3%29x+-+%283%2F5%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282%2F3%29x+-+%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that I presume you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%2Ax ALIGN=MIDDLE  ALT=\"%282%2F3%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > and not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3x ALIGN=MIDDLE  ALT=\"2%2F3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is what you wrote<BR>\n" );
document.write( "if the rules of algebraic convention are followed.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "There are four steps to finding an inverse of the function. These steps are:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1. Replace f(x) with y<BR>\n" );
document.write( "2. Then replace y by x and also change x to y<BR>\n" );
document.write( "3. Solve for y<BR>\n" );
document.write( "4. Finally replace y by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's do it by following these 4 steps. Start with the given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%282%2F3%29x+-+%283%2F5%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%282%2F3%29x+-+%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Replace f(x) by y to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F3%29x+-+%283%2F5%29 ALIGN=MIDDLE  ALT=\"y+=+%282%2F3%29x+-+%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Step 1 is done.  Next do step 2 by changing y to x and also changing x to y.  When you<BR>\n" );
document.write( "do that the equation from step 1 becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282%2F3%29y+-+%283%2F5%29 ALIGN=MIDDLE  ALT=\"x+=+%282%2F3%29y+-+%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Step 2 is now done.  On to step 3 which tells you to solve for this equation for y. <BR>\n" );
document.write( "You can isolate the term that contains y. Do that by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5%29 ALIGN=MIDDLE  ALT=\"3%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides of <BR>\n" );
document.write( "the equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%283%2F5%29+=+%282%2F3%29y+-%283%2F5%29+%2B+%283%2F5%29 ALIGN=MIDDLE  ALT=\"x+%2B+%283%2F5%29+=+%282%2F3%29y+-%283%2F5%29+%2B+%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that the terms <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5 ALIGN=MIDDLE  ALT=\"-3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > cancel each other on the right side so <BR>\n" );
document.write( "the equation is reduced to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%283%2F5%29+=+%282%2F3%29y ALIGN=MIDDLE  ALT=\"x+%2B+%283%2F5%29+=+%282%2F3%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can get rid of the denominator 5 on the right side by multiplying all the terms on<BR>\n" );
document.write( "both sides of this equation by 5.  Multiplying everything by 5 results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+%2B+3+=+%2810%2F3%29%2Ay+ ALIGN=MIDDLE  ALT=\"5x+%2B+3+=+%2810%2F3%29%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now get rid of the denominator of 3 on the right side by multiplying everything on both<BR>\n" );
document.write( "sides by 3 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+%2B+9+=+10y ALIGN=MIDDLE  ALT=\"15x+%2B+9+=+10y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now solve for y by dividing both sides by 10 and the result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x+%2B+9%29%2F10+=+y ALIGN=MIDDLE  ALT=\"%2815x+%2B+9%29%2F10+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Step 3 is done.  Now replace y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the answer becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29=+%2815x+%2B+9%29%2F10 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29=+%2815x+%2B+9%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Presuming that I interpreted your problem correctly, this is the answer you were asked to<BR>\n" );
document.write( "find.  I'm not sure where you got the answer that you did. Even if I interpreted it incorrectly,<BR>\n" );
document.write( "the four step process is correct, and you can use this same method to solve any problem with<BR>\n" );
document.write( "inverting a function.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );